Math 5A Course Description

Math 5A is the second course of a two quarter sequence in Differential Equations and Linear Algebra. The text is Farlowe, et al. 'Differential Equations and Linear Algebra.'

In differential equations, the emphasis is divided between quantitative and qualitative aspects

- The emphasis is on the simplest cases of methods for closed form solutions with e.g. Undetermined Coefficients. Because of this, we emphasize accuracy of solutions. Students should be taught to verify that their answer really does solve the ODE.

- The phase plane, equilibrium points and their stability are important.

In linear algebra, proofs of theorems and large scale hand computations are de-emphasized in order to tie the material more closely to the application at hand: systems of linear differential equations. Again, this means we emphasize the accuracy of those calculations which are done. Students should verify that, for example, eigenvectors really are correct.

5A covers three and a half chapters in the text. Times given below are very approximate and do not include exams; we have not yet taught this version of the syllabus.

Appendix CN Complex numbers (~ 1 lecture) Students need to know exp(x+iy) = exp(x)(cos(y) + i sin(y)).


Chapters & Topics

4. 2nd Order Linear ODEs (~ 2.5 weeks)
     Section 4.7 is mostly optional, except the conversion from 2nd order ODEs to first order systems of ODEs, which provides the connection to chapter 6.

5. Linear Transformations (~ 2.5 weeks)
     In Section 5.3 'Eigenvalues and Eigenvectors' you might want to motivate the abstract definition of eigenvector by looking ahead to Section 6.2, p.333 and 334.
     Section 5.4 'Diagonalization' contains a subsection 'The Right Point of View for DEs' which provides the connection between the linear algebra theory and the (inhomogeneous) linear system of ODEs application.

6. Linear Systems of DEs (~ 2.5 weeks)
     Section 6.4 'Decoupling a linear DE system' connects up with chapter 5 as mentioned above.

7. Nonlinear Systems (~ 1 week)
     Cover only 7.1 Nonlinear Systems and 7.2 Linearization.